The Empirical Process Approach for Semiparametric Two-Sample Models with Heterogeneous Treatment Effect
提出两类半参数两样本模型，用于比较可能存在异质性处理效应的两组样本，并利用经验过程方法构建强近似，推导出广义最小二乘估计量，该估计量在位置尺度模型下渐近有效。
SUMMARY Two types of semiparametric model are proposed for comparing two samples with possibly heterogeneous treatment effects. One model is a two-sample location-scale model which assumes that the Q-Q-plot of the two distributions involved is linear; the other is the class of two-sample transformation models which assume parametric forms for a probability plot—the receiver operating characteristic curve. The empirical process approach is used to construct strong approximations for the empirical curves of both types of plot and a convenient generalized least squares (GLS) estimator is derived. The approximate finite sample precision of the estimators can be easily evaluated. Asymptotically, the GLS estimator is shown to be efficient for the first model. A difficulty involved in developing the theory of asymptotic efficiency is discussed for the transformation models. The GLS estimator is shown numerically to approach the Fisher information bound for the proportional hazards model.